Solving by Combining Like Terms
5h + 2 + 2h = 23
h = 3
Simplify: 8b + 3b
11b
2x + 8 = 2(x + 4)
Infinitely many solutions
WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?
n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.
3b + b - 8 = 4
b = 3
Simplify: 19x - 24x
-5x
4x + 1 = 2(2x+3)
No solution
Ms. Garrisi bought 7 Taylor Swift t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Taylor Swift t-shirts did Ms. Garrisi buy?
n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99
3a + 12 - 6a = -9
a = 7
Simplify: 3 + 5(a + 4)
5a + 23
3x + 1 = 3(x - 1) + 4
Infinitely many solutions
Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.
-6 = -3y + 4 + 5y
y = -5
Simplify: - (2b - 4) + 5b
3b + 4
4x + 2x - 5 = 7x - 1
One solution: x = -4
Mr. Tribbiani goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?
r - cost of a bag of raisins 17r + 2.97 = 34.76
r = 1.87 Each bag of raisins cost $1.87
78 = 3c + 12 - c + 4
c = 31
-13(-4 - 2a) = 208
a = -6
Simplify: 7(t + 8.5) - 5t + 4
2t + 63.5
3x + 7x + 1 = 2(5x + 1)
No solution
When you count by ones from many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?
n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.